(1+z)(4z-3)=0

Solution for (1+z)(4z-3)=0 equation:

Simplifying
(1 + z)(4z + -3) = 0

Reorder the terms:
(1 + z)(-3 + 4z) = 0

Multiply (1 + z) * (-3 + 4z)
(1(-3 + 4z) + z(-3 + 4z)) = 0
((-3 * 1 + 4z * 1) + z(-3 + 4z)) = 0
((-3 + 4z) + z(-3 + 4z)) = 0
(-3 + 4z + (-3 * z + 4z * z)) = 0
(-3 + 4z + (-3z + 4z2)) = 0

Combine like terms: 4z + -3z = 1z
(-3 + 1z + 4z2) = 0

Solving
-3 + 1z + 4z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-1 + -1z)(3 + -4z) = 0

Subproblem 1
Set the factor '(-1 + -1z)' equal to zero and attempt to solve:

Simplifying
-1 + -1z = 0

Solving
-1 + -1z = 0

Move all terms containing z to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + -1z = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1z = 0 + 1
-1z = 0 + 1

Combine like terms: 0 + 1 = 1
-1z = 1

Divide each side by '-1'.
z = -1

Simplifying
z = -1
Subproblem 2
Set the factor '(3 + -4z)' equal to zero and attempt to solve:

Simplifying
3 + -4z = 0

Solving
3 + -4z = 0

Move all terms containing z to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -4z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4z = 0 + -3
-4z = 0 + -3

Combine like terms: 0 + -3 = -3
-4z = -3

Divide each side by '-4'.
z = 0.75

Simplifying
z = 0.75
Solution
z = {-1, 0.75}